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Brennan was born in Castlebar, Ireland, and moved to Melbourne, Australia in 1861 with parents. He started his career as a watchmaker and a few years later was articled to Alexander Kennedy Smith, a renowned civil and mechanical engineer of the period. He served as a sergeant in the Victorian Engineers under the command of Captain J. J. Clark. Brennan invented the idea of a steerable torpedo in 1874, from observing that if a thread is pulled on a reel at an angle with suitable leverage, the reel will move away from the thread side. Brennan spent some years working out his invention, and received a grant of £700 from the Victorian government towards his expenses. He patented the Brennan Torpedo in 1877. The idea was trialled at Camden Fort near Crosshaven, Cork, Ireland.[1]

Brennan went to England in 1880 and brought his invention before the War Office. Sir Andrew Clarke alerted the authorities to the possibilities of the torpedo if used in the defence of harbours and channels, and the patent was eventually bought for a sum believed to be more than £100,000. In 1887 Brennan was appointed superintendent of the Brennan torpedo factory, and was consulting engineer 1896–1907.

He did much work on a monorail locomotive which was kept upright by a gyrostat. In 1903 he patented a gyroscopically-balanced monorail system that he designed for military use; he successfully demonstrated the system on 10 November 1909, at Gillingham, England, but fears that the gyroscopes might fail prevented adoption of the system for widespread use.[2]

From 1916 to 1919 Brennan served in the munitions inventions department. From 1919 to 1926 he was engaged by the air ministry in aircraft research work at the Royal Aircraft Establishment, Farnborough,[3] and gave much time to the invention of a helicopter. The government spent a large sum of money on it, but in 1926 the air ministry gave up working on it, much to Brennan's disappointment.[4]

Brennan's gyroscopically balanced monorail on a demonstration run.

In January 1932 he was knocked down by a car at Montreux, Switzerland, and died on 17 January 1932. He had married Anna Quinn (died 1931) on 10 September 1892. He was survived by a son and a daughter. Brennan was created a Companion of the Order of the Bath in 1892, and was foundation member of the National Academy of Ireland in 1922.[3]